Speaking on his Call Clegg radio phone-in on LBC 97.3, he said: "I find the whole thing so mysterious. The Labour leadership appear to be puppets on a string run by these trade union bosses.

"How these union bosses get elected, how they raise money, how they disperse money is a complete and utter mystery. Something seriously dodgy clearly happened in Falkirk. It is really time the Labour leadership come clean with people about exactly what happened so people – given that this is a party that wants to run the country from 2015 – people know what kind of party it is."

Labour launched an internal inquiry in July into allegations that Unite tried to fix the Falkirk selection for its favoured candidate, but the investigation was closed in September after finding no evidence that rules were breached.

Miliband has made the claims of irregularities against Unite in Falkirk a key battleground of his leadership but has refused to publish the internal report.

It follows months of criticism of Unite, which has given Labour £8m since the last election, for launching a party recruitment drive to ensure the safe passage of its candidate Karie Murphy.

Miliband is pressing ahead with plans to reform Labour's financial links with the unions, so that affiliation fees are paid only in relation to members who choose to support the party. He will seek approval for the new arrangements at a special conference in the spring.

The Conservative party chairman, Grant Shapps, said on Wednesday: "Despite Ed Miliband's promises of change, nothing has changed. The union bosses still buy the policies, fix the selections and pick the leader. It's the same old Labour.

"If Ed Miliband is serious about standing up to Len McCluskey, he should re-open his inquiry into the Unite union's attempt to fix the Labour party selection in Falkirk. If he's too weak to govern his party, Ed Miliband is too weak to govern the country, too weak to cut the deficit and too weak to fix the welfare system."